Read closely, "Adieu" is told by a pet, most likely a dog, though the poem never names the animal. The clues are the cage, the rug, and the fierce loyalty to a "master." A thunderstorm rolls in, the lights go out in the master's home, and the speaker is alone and terrified. All it wants is the warmth of his love.
The speaker breaks out of the cage and runs to the house, but the door is shut. In panic it keeps running, and the line "I should have seen the well" tells us, quietly and without fuss, that it has fallen in. The title now reads as a goodbye.
What makes the ending so sad is that the speaker never complains. In the cold dark it imagines its master's arms and kisses, and when the sky clears it hopes he is happy, dreaming of it. The mood moves from fear to heartbreak, softened by a tender, unselfish love.